They’ve explained what this is & that it doesn’t affect your credit score in a blog post -
When you sign up for a Monzo account or upgrade your account, we run something called a “quotation search.” Sometimes known colloquially as a “soft credit check” or “soft footprint,” this type of search will not affect your credit score.
It was introduced by legislators to allow people to shop around for credit, without affecting their credit scores. It’s the kind of search carried out when you shop around for loans or mortgages on a price comparison site like Money Supermarket or Go Compare. Quotation searches like this will appear on your credit record, but lenders are not allowed to take them into account when making lending decisions.
When you upgrade your account, we run this type of check to determine whether or not we’d be able to offer you an overdraft, in case you want one in the future.
Once your upgraded Monzo account is open, we also notify our credit reference agency that you have a bank account with us.
Opening a bank account should not affect your credit score, unless you get an overdraft, or you’ve opened lots of accounts in a short period of time.
An overdraft can affect your credit score positively or negatively, depending on how you use it. Overdrafts on Monzo are 100% opt-in, meaning you can choose whether to have one or not. They won’t affect your credit score unless you explicitly switch on your overdraft.